Download p 11 Refraction application note and questions

Applying Knowledge of Refraction and Total Internal Reflection
The knowledge you now have of refraction and total internal reflection makes it possible to understand many interesting natural phenomena and the operation of several optical instruments. This reading gives some examples from both areas.
Atmospheric Refraction
Several interesting natural phenomena involve refraction of light by the atmosphere. Refraction of sunlight is one of these. Because of refraction, you can see the sun for several minutes before it actually rises above the horizon in the morning. also, you can see it for several minutes after it has actually set below the horizon in the evening. Figure P11.1 below represents an observer standing on the north pole looking in the direction of the sun when the sun is actually in position A. Although the sun is really below the horizon, it can still be seen by the observer. The optical density of air is greater than the optical density of the near vacuum of space. Therefore the light slows down as it enters the atmosphere. This decrease in speed causes the refraction shown in the illustration. Since the atmosphere and space have no definite interface, no abrupt refraction occurs as you observed at the glass­air interface. Instead, a gradual bending occurs since the air gradually becomes more dense as the earth is approached.
Apparent position of sun
B
Figure P11.1
Refraction of sunlight causes an apparent change in the position of the sun. The diagram is not to scale; the bending is exaggerated. The true angle between the actual position and apparent position is not quite 2o.
A
Actual position of sun
Atmospheric refraction is also responsible for a phenomenon known as the moon illusion. You have likely noticed how large the moon appears to be when it is near the horizon. It also appears to have an elliptical (football­like) shape. This illusion is caused by the fact that rays of light from the lower part of the moon are refracted more than rays from the upper part.
Atmospheric refraction causes the twinkling of stars. The atmosphere is made up of many moving layers of air. These layers are of different temperatures and,therefore, of different densities. As a result, light from a star is refracted from side to side as it passes through these layers. Since the layers are moving, the stars appear to twinkle. The twinkling of stars hinders careful observation by astronomers. Therefore they generally make their observations on cold, calm winter nights when there is usually less movement in the atmosphere. Astronomers often locate their observatories high in mountains to get above some of the atmosphere. For many years some astronomers have avoided the atmosphere completely by sending telescopes and other equipment above the atmosphere in rockets and balloons.
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You have likely seen heat waves. When an object is viewed through the air above a fire, hot pavement, or other heat sources, the object has a distorted, wiggling appearance. Many people refer to this phenomenon as heat waves. However, heat waves cannot be seen. You are simply seeing the effects of atmospheric refraction. The air just above a heat source is warmer and, therefore less dense than the air further away. As a result, the light from the object you are viewing is refracted as it enters the warm air. Since the warm air is moving, the object appears to be distorted and wiggling.
A mirage is caused by total internal reflection. The most common mirage is the apparent layer of water that we see on paved roads in hot weather. The air next to the pavement becomes warm and, therefore, less dense than the air above it. As a result, light from the sky passes from a more dense to a less dense medium. If the light meets the less dense air at an angle of incident that is greater than the critical angle for this interface, total internal reflection occurs and the observer sees an image of the sky as shown in figure P11.2. The human eye cannot detect the change in direction of the light on reflection. Therefore the image of the sky appears to be on top of the pavement causing the wet appearance.
Figure P11.2
A mirage is caused by total internal reflection.
Observer
cool air
normal
light from the sky
warm air
pavement
Mirages are told of thirsty desert travelers who thought they saw pools of water in the sand or trees in the ground (fig P11.3). It would be incorrect to tell such people that their imaginations were fooling them. Mirages are real. They are formed by real rays of light and have often been photographed.
A less common type of mirage occurs when objects that are beyond the horizon appear to be lifted into view. Desert travelers have reported seeing a ship in the air above the sand or an oasis in the midst of a flat dry plain. This type of mirage is not easily explained but it is generally thought to be caused by a complex series of reflections and refractions at the surface of a warm layer of air.
Our eye takes light back to the place where we think they met ­ where they originated because we believe that light travels in straight lines.
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Optical devices which use refraction and internal reflection
The periscope is one optical device that uses total internal reflection (fig P11.4). The two prisms act as plane mirrors to change the direction of light. The prisms are arranged so that total internal reflection occurs. Prisms are used instead of mirrors for two main reasons. First, the reflecting surface of the prism is on the inside where it cannot be easily damaged. Second, the prism reflects more of the incident light than does a mirror. Thus the image will be brighter.
Total internal reflection will occur twice in a 90o triangular prism if the incident light meets the hypotenuse at a 90o angle and near one end. This knowledge has been used for the designing of binoculars and other optical instruments that use "folded optics". One factor that determines the magnifying power of an optical instruments is the distance the light travels in the instrument. In order to avoid very long instruments, the light is bent back and forth ("folded") using prisms. Figure P11.5 shows how this is done in binoculars. the same principle is used in some telescopes and telephoto lenses for cameras.
incident ray
90o triangular prism
90o triangular prism
Observer
Figure P11.4
A periscope uses 90o triangular prisms to reflect light
Figure P11.5 Binoculars contain prisms to increase the length of the path that light travels in the instrument.
Refraction and Apparent Depth
When light refracts or is internal reflected, our brain will perceive the image to be at a different location than it really is. Whether it is a mirage or a the setting moon, the light tricks our brain. An excellent example of this occurs when we see an object in the with water. The light bends on the water air interface. As the angle of incidence increases, the apparent location makes the object seem higher in the water than it really is. This is referred to as apparent depth. See figure P11.6
Figure P11.6
The chest appears to be much closer to the surface of the water because of how the rays bend as they enter air.
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Try this!
Place a coin on the bottom of an opaque cup. Place the cup on a surface. Slide the cup away, stopping when you can't see the coin anymore. Without changing this position, fill the cup with water. Why can you now see the coin? Has the coin changed position?
Homework Questions
1. a) Explain how atmospheric refraction makes it possible for us to see the sun even though it may actually be below the horizon.
b) The sun's rays are refracted whenever they enter the atmosphere at an oblique angle. However, the refraction is greatest when the sun is at the horizon. Why is this so? (There are two reasons. You should be able to discover one of them by studying Figure P11.1)
2a) What is the moon illusion? What causes it?
b) What causes the twinkling of stars?
3a) What causes heat waves?
b) Explain in your own words why a pavement often appears wet on a hot day.
4a) Draw a sketch of a periscope that uses plane mirrors instead of prisms. Show the light path.
b) What advantages do prisms have over mirrors?
c) Copy the figure of the periscope and use it to show how the image of an object viewed through a periscope is erect.
5a) What is folded optics?
b) What advantage does folded optics offer?
c) Name three optical devices that use folded optics.
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